ESTIMATING ADVECTIVE TENDENCIES FROM FIELD-MEASUREMENTS

The ability to estimate horizontal advective tendencies of environment al variables from measurements at a finite set of observation points h as been evaluated. The observation points include a central point plus from three to six boundary points at a mean distance of R(0). Two met hods of estimation were considered: either by a numerical approximatio n to the flux line integral, or by integrating a quadratic fit to the field function (the latter if there are five of more boundary points). Errors arise from random instrument errors (or turbulent fluctuations ) and because of truncation errors. The latter results from a mismatch between the spatial distribution of the field being considered and th e assumptions underlying the approximation algorithm. Both types of er rors were considered. Random errors were considered using standard the ory for the propagation of errors. Terms of the Fourier series were us ed as test functions to study truncation errors. The standard against which estimates were evaluated was multipoint numerical integrations. For truncation errors, the significant result is that the use of a tri angle of boundary points yields estimates close to 10% of the exact va lue only for a wavelength greater than about 20R(0); if cells have rad ius of 100 km, that would be a wavelength of 2000 km; for a square, th e estimates are better than 10% at a wavelength of about 7R(0) (700 km ); and for a pentagon, the estimates are less than 10% for the smalles t nonaliasing wavelength. For this application, the use of a quadratic fit added little to accuracy; for a symmetrical array of points, the quadratic term does not contribute to the advective tendency. When one considers joint random and truncation errors, the general result is t hat truncation errors are more important than random errors for small wavelengths, and the reverse for large wavelengths. The results indica te that there is a substantial gain in going from three to four or fiv e boundary points; the improvement for each further increment is less dramatic. It is recommended that simple algorithms be augmented by the use of remotely sensed finescale observations of surrogate and by occ asional periods of observations at higher spatial density.